A course in analysis
 Responsibility
 Niels Jacob, Kristian P. Evans (Swansea University, UK).
 Publication
 New Jersey : World Scientific, [2016]
 Physical description
 volumes : illustrations ; 26 cm
At the library
Science Library (Li and Ma)
Stacks
Library has: v.14
Call number  Status 

QA300 .J27 2016 V.1  Unknown 
QA300 .J27 2016 V.2  Unknown 
QA300 .J27 2016 V.3  Unknown 
QA300 .J27 2016 V.4  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Jacob, Niels.
 Contributor
 Evans, Kristian P.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Introductory Calculus: Numbers  Revision The Absolute Value, Inequalities and Intervals Mathematical Induction Functions and Mappings Functions and Mappings Continued Derivatives Derivatives Continued The Derivative as a Tool to Investigate Functions The Exponential and Logarithmic Functions Trigonometric Functions and Their Inverses Investigating Functions Integrating Functions Rules for Integration Analysis in One Dimension: Problems with the Real Line Sequences and their Limits A First Encounter with Series The Completeness of the Real Numbers Convergence Criteria for Series, badic Fractions Point Sets in Continuous Functions Differentiation Applications of the Derivative Convex Functions and some Norms on n Uniform Convergence and Interchanging Limits The Riemann Integral The Fundamental Theorem of Calculus A First Encounter with Differential Equations Improper Integrals and the GAMMAFunction Power Series and Taylor Series Infinite Products and the Gauss Integral More on the GAMMAFunction Selected Topics on Functions of a Real Variable.
 (source: Nielsen Book Data)
 Summary

Volume 1 covers the content of two typical modules in undergraduate course for mathematics: Part 1: Introductory calculus Part 2: Analysis of functions of one variableThese two parts are divided into 32 chapters. Part 1 begins with an overview of a set of real numbers: rational and irrational. This is accompanied by a discussion of arithmetic rules, inequalities, absolute values. Doing this, the authors, in a clever way, introduce elements of a set theory using Cantor's approach. This is followed by the definition of a function and discussion of operations on functions. From this they move to differential and integral calculus and their applications.Part 2 contains rigorous proofs of theorems from Part 1. In particular, they introduce the order structure on a real line using axioms of an ordered field. It is worth mentioning that Part 2 contains elements of topology obviously on real line and a good insight on convex functions. The convex functions relate Analysis to linear spaces equipped with norm. Finally, to close Part 2 the authors supply a number of Appendices, among them Appendices on logic, set theory and Peano axioms.Remarkably, Volume 1 contains 360 problems with complete solutions.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Beginning date
 2016
 ISBN
 9789814689083 (v. 1 : hardcover : alk. paper)
 9814689084 (v. 1 : hardcover : alk. paper)
 9789814689090 (v. 1 : pbk : alk. paper)
 9814689092 (v. 1 : pbk : alk. paper)
 9789813140950 (v. 2 : hardcover : alk. paper)
 9789813221598 (v. 3 : hardcover : alk. paper)